Unusual Hall Effect Anomaly in MnSi under Pressure

We report the observation of a highly unusual Hall current in the helical magnet MnSi in an applied pressure $P=6–12\mathrm{kbars}$. The Hall conductivity displays a distinctive stepwise field profile quite unlike any other Hall response observed in solids. We identify the origin of this Hall current with the effective real-space magnetic field due to chiral spin textures, which may be a precursor of the partial-order state at $P>14.6\mathrm{kbar}$. We discuss evidence favoring the chiral spin mechanism for the origin of the observed Hall anomaly.

Figure 1

(Main panel) Curves of $-{\rho }_{yx}$ in MnSi at 11.4 kbar revealing a large Hall anomaly in the field range $0.1<H<0.45\mathrm{T}$ for several $T<T_C$ ($T_C=11.3\mathrm{K}$), with $\mathbf{H}$ nominally along (111). The anomaly (electronlike in sign) arises from a new contribution ${\sigma }_{xy}^C$ to the total Hall conductivity. In the phase diagram (inset), the shaded region is where ${\sigma }_{xy}^C$ is resolved. $T_C$ was determined from $\rho$ vs $T$. Data from Samples 1 and 2 are shown as solid and open squares, respectively. The non-Fermi liquid (NFL) region is shaded dark gray (adapted from Ref. 2).

Figure 2

Curves of ${\rho }_{yx}$ extending to 7 T showing the relation of the Hall anomaly to other Hall terms (at the applied $P=8.5\mathrm{kbar}$, $T_C=16.4\mathrm{K}$). At 5 K, the holelike ${\sigma }_{xy}^N$ dominates ${\rho }_{yx}$ to produce an $H$-linear background. At $T=10$ and 15 K, at which the Hall anomaly is observed as sharp negative spikes, the AHE term ${\rho }_{yx}^A={\sigma }_{xy}^A{\rho }^2$ grows in prominence as $\rho$ increases. Above $T_C$ (20 and 25 K), the Hall anomaly vanishes, while ${\rho }_{yx}^A$ continues to increase in magnitude. The reduced temperature $t=T/T_C$ is shown in parenthesis for each curve.

Figure 3

Panel (a) Curves of ${\sigma }_{xy}$ vs $H$ at $P=11.4\mathrm{kbar}$ at selected $T$. The Hall anomaly ${\sigma }_{xy}^C$ is prominent between 11 and 5 K between the fields $H_1$ and $H_2$. At 2.5 K, only the normal term ${\sigma }_{xy}^N$ is observed. The inset shows the itinerant spin $\mathbf{s}$ aligned with the local moment ${\mathbf{S}}_i$ on site $i$ by a large $J_H$. As the electron closes the path 1-2-3-1, it acquires a Berry phase ${\varphi }_B$. Panel (b) Curves of the MR $\Delta \rho /\rho$ vs $H$ at selected $T$ at 11.4 kbar (curves are offset for clarity). Below $T_C$ (11.3 K), anomalies indicate fields $H_1$ (up arrows), $H_2$ (down arrows), and $H_s$. By comparison, the MR is nearly zero below $H_s=0.6\mathrm{T}$ at ambient pressure (thin curve at 25 K).